Question: Simplify the following expression: $ r = \dfrac{-2}{7} + \dfrac{-5p - 1}{5p - 8} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5p - 8}{5p - 8}$ $ \dfrac{-2}{7} \times \dfrac{5p - 8}{5p - 8} = \dfrac{-10p + 16}{35p - 56} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{-5p - 1}{5p - 8} \times \dfrac{7}{7} = \dfrac{-35p - 7}{35p - 56} $ Therefore $ r = \dfrac{-10p + 16}{35p - 56} + \dfrac{-35p - 7}{35p - 56} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-10p + 16 - 35p - 7}{35p - 56} $ $r = \dfrac{-45p + 9}{35p - 56}$